Why are Banks Exposed to Monetary Policy?

Transcription

1 Why are Banks Exposed to Monetary Policy? Sebastian Di Tella and Pablo Kurlat Stanford University Bank of Portugal, June 2017

2 Banks are exposed to monetary policy shocks Assets Loans (long term) Liabilities Deposits (short term) Net Worth Maturity mismatch interest rate risk Transmission channel of monetary policy Begenau, Piazzesi & Schneider (2014): banks use derivatives (interest rate swaps) to increase exposure to interest rate risk

3 Why do banks choose this exposure? Focus on banks as providers of liquidity Banks exposure to interest-rate risk is part of dynamic hedging strategy deposit spreads co-move with interest rate (Drechsler et al. 2015) capital gains offset flow returns implement with maturity-mismatched balance sheet Fits level, time series, and cross-section of maturity mismatch

4 Technology and Preferences Fixed capital stock k produces constant output flow y = ak Households and bankers with the same preferences: ( f (x,u) = ρ(1 γ)u log(x) 1 ) 1 γ log((1 γ)u) Epstein-Zin with EIS=1 and RRA γ Currency-and-deposits in the utility function: x: Cobb-Douglas aggregator of c (consumption) and m (money) x(c,m) = c β m 1 β m: CES aggregator of h (real currency) and d ( real deposits). Elasticity ǫ m(h,d) = (α 1 ǫ h ǫ 1 ǫ ) +(1 α) 1 ǫ ǫ 1 ǫ 1 ǫ d ǫ

5 Monetary Policy Currency supplied via (stochastic) lump-sum transfers Flexible prices Reverse-engineered to produce stochastic process for interest rates: di t = µ(i t )dt+σ(i t )db t B is standard Brownian Motion Friedman rule is optimal it = 0 In quantitative section, Cox-Ingersoll-Ross process: µ(i) = λ(i ī) σ(i) = σ i

6 Deposits Bankers can issue deposits up to leverage limit d S φn regulatory constraint/economic condition for deposits to be liquid prevents infinite supply of deposits makes bankers net worth an important state variable In equilibrium deposits pay (endogenous) nominal rate i d t < i t. Spread: s t = i t i d t > 0

7 Markets Complete markets real interest rate: rt = i t µ p,t trade exposure to B at price πt Capital and lump-sum transfers priced by arbitrage No assumptions on what assets banks hold

8 Household and Banker s Problems Household s.t. ( dw t = w t max w,x,c,m,h,d,σ w U (x) ) r t +σ w,t π t ĉ t ĥti t ˆd ( t it i d ) t dt+σ w,t db t }{{} s t m t = (α 1 ǫ h ǫ 1 ǫ t x t = c β tm 1 β t +(1 α) 1 ǫ d ǫ 1 ǫ t w t 0 ) ǫ ǫ 1 Banker: same except bankers earn spread on deposits issued: dn ( t = r t +σ n,t π t ĉ t ĥti t n ˆd ) t s t +ˆd S t s t dt+σ n,t db t t ˆd S t φ

9 Equilibrium Definition State variables: i: current level of interest rates z = n : fraction of total wealth held by bankers n+w Equilibrium 1. Value functions and policy functions 2. Prices 3. Law of motion for z such that 1. Value and policy functions solve household & banker s problem 2. Markets clear 2.1 goods 2.2 currency 2.3 deposits 2.4 capital 3. Law of motion for z is consistent with policy functions

10 Deposit Spread From the FOCs and market clearing for deposits we get a static equation for the deposit spread: ( ) ǫ ι(i,s) (1 α) (1 β) χ(i,s) ρ = φ z s ι(i,s) χ(i, s) }{{}}{{}}{{}}{{}}{{} d m x d m x ω z n n ω where ι and χ are CES and Cobb-Douglas price indices Solve for spread s(i,z) decreasing in z increasing in i if ǫ > 1 ι(i,s) = ( αi 1 ǫ +(1 α)s 1 ǫ) 1 1 ǫ ( ) 1 β χ(i,s) = (β) β ι(i,s) 1 β

11 Deposit Spread s(i,z) OLS regression of spread (Drechsler et al. [2014]) on i (Libor 6m) and z (Flow of Funds): s = 0.3% i 0.99 z (0.22%) (0.028) (0.25) s = 0.3% i 4.07 i z (0.44%) (0.17) (2.02) (0.32)

12 Exposure of z to monetary shocks B Value function has form Vt h (w) = (ζ tw) 1 γ 1 γ Vt b (n) = (ξ tn) 1 γ 1 γ for household for banker the endogenous ζ t and ξ t capture forward-looking investment opportunities FOCs for risk exposure: σ w = π γ + 1 γ σ ζ γ }{{} household σ n = π γ + 1 γ σ ξ γ }{{} banker Premium + dynamic hedging Income vs. substitution. If γ > 1, income effect dominates

13 Exposure of z to monetary shocks B Therefore, exposure of z n n+w : σ z = (1 z)(σ n σ w ) = σ z = (1 z) 1 γ γ (σ ξ σ ζ ) How banks share of wealth z reacts to an increase in interest rates depends on: how relative investment opportunities ξ/ζ react: σξ σ ζ > 0 income vs substitution effects: 1 γ γ < 0 Dynamic hedge: banks are willing to take a loss when interest rates rise because they expect large spreads looking forward

14 Parameter Values Meaning Value Remarks γ Risk aversion 10 Bansal & Yaron (2004) ī Mean interest rate 3.5% σ Volatility of i m LIBOR λ Mean reversion of i Volatility of 10-year rates ρ Discount rate consumption wealth Checking + Savings Net Worth φ Leverage 8.77 α CES weight on currency 0.95 Time series of s(i,z) β CD consumption share 0.93 (Drechsler et. al. 2014) ǫ Elasticity currency / deposits 6.6 σ a Volatility of TFP Risk free rate τ Tax on bank equity Average z

15 Deposit Spread s(i,z)

16 Banks exposure to movements in interest rates: σn /σi

17 Maturity Mismatch T Implement σ n with traditional balance sheet: assets: zero coupon nominal bond of maturity T liabilities: short-term nominal liabilities (e.g. deposits) Compute maturity mismatch: Price bonds of every maturity p B (i,z;t) Compute exposure of each bond to interest rates σp B (i,z;t) Find maturity T such that σ n = (1+φ)σ pb (i,z;t)

18 Maturity Mismatch Higher maturity mismatch when i and z are low: reflects larger sensitivity of s(i,z) to changes in i in that region. OLS: T = i 1.9 z (0.1) (6.8) (0.4)

19 Quantitative evaluation: time series Construct banks maturity mismatch using Call Reports (English et al. (2012)) record contractual or repricing maturity of assets and liabilities, and substract asset-weighted median across banks compare with model predictions based on time series for i and z

20 Maturity mismatch time series Levels: avg. maturity mismatch data: 4.4 yrs; model: 3.9 yrs Time pattern: maturity mismatch high when i low; correlation: 0.77

21 Cross sectional evidence Model: banks with more deposits should have a larger maturity mismatch Re-solve banker s problem with different φ = d/n; for each φ compute the whole time series of maturity mismatch, and take average Regress maturity mismatch on φ: β = 0.42 Same regression in the data Median OLS Constant (0.0023) (0.063) φ (0.0004) (0.013) N 10, , 351

22 Real shocks under inflation targeting Shocks to expected growth rate µ a,t : dµ a,t = λ(µ a,t µ a )dt+σ µ a,t µ min a,t db t µ a,t Central bank adjusts currency supply to keep inflation constant (e.g. 2%): i t = r t + µ p Negative growth shock low eq. real interest rate low nominal interest rate Set parameters to match volatility of interest rates Requires large and persistent growth shocks

23 Maturity Mismatch with Real Shocks Levels: avg. maturity mismatch data: 4.4 yrs; model: 4.7 yrs Time pattern: maturity mismatch high when i low; correlation: 0.51

24 Conclusions Dynamic hedging of deposit spreads explains banks interest-rate exposure average, time pattern, cross-sectional pattern Does not depend on why interest rates move: monetary and real shocks under inflation targeting Banks maturity mismatch amplifies the effects of monetary policy shock on the cost of liquidity Implications for other types of risk exposure (e.g. credit spreads)

25 Extra: Static Decisions Currency-deposit choice (from CES): unit cost of m is d ( ι ǫ h ( ι ) ǫ m s) = (1 α) m = α i ι(i,s) = ( αi 1 ǫ +(1 α)s 1 ǫ) 1 1 ǫ Consumption-money choice (from Cobb-Douglas): c = β(χx) ιm = (1 β)(χx) unit cost of x is ( ) 1 β χ(i,s) = (β) β ι(i,s) 1 β

26 Extra: Dynamic Decisions FOC for ˆx is the same for household and banker: ˆx t }{{} x wealth χ t }{{} unit cost of x = ρ IES = 1 spending = ρ wealth Goods market clearing: ak }{{} output = β }{{} consumption spending ρ }{{} spending wealth ω t }{{} total wealth ω t n t +w t = ak βρ Cobb-Douglas + IES = 1 Constant wealth